Question 3: Solow model Suppose the production function is written as follows: =^0.05^0.05 Suppose that saving rate (s) is 0.3, population growth rate (n) is 0.05, and capital depreciation rate (d) is 0.05. (note: when you write your equations, be careful to distinguish capitalized characters and non-capitalized characters!)

3-1. Derive the per-capita production function (i.e. =Y/L and =K/L). 3-2. Provide the key equation of the Solow model on capital accumulation per capita. Then, impute key parameter values. (you do not have to derive the key equation) 3-3. Draw a key graph for the Solow model. (hint: on y-axis and for x-axis. Then draw per- capita production function. You also need to draw two additional curves derived from the capital accumulation equation) 3-4. What is the steady-state level of per-capita capital? Solve the model and obtain the number. What is the economic growth rate when the economy is under the steady-state? 3-5. Suppose at the first period of the economy, = 4. What happens to the economy? Use a graph to show your answer. 3-6. Suppose the economy now has higher population growth rate. What happens to the steady state? What happens to the economic growth rate? Discuss with a graph.